```python
import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline


_cpp_source = """
#include <torch/extension.h>
torch::Tensor min_softmax_cuda(torch::Tensor x);
"""

_cuda_source = r"""
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <c10/cuda/CUDAGuard.h>
#include <c10/cuda/CUDAException.h>
#include <cuda_runtime.h>
#include <cmath>
#include <cstdint>

template<int CHANNELS>
__global__ void min_softmax_kernel(
    const float* __restrict__ x,
    float* __restrict__ out,
    const int64_t spatial,
    const int64_t depth)
{
    const int64_t p =
        static_cast<int64_t>(blockIdx.x) * blockDim.x + threadIdx.x;
    if (p >= spatial) {
        return;
    }

    const int64_t batch = blockIdx.y;
    const int64_t channel_stride = depth * spatial;
    const float* batch_input = x + batch * CHANNELS * channel_stride + p;

    float values[CHANNELS];
    float maximum = -CUDART_INF_F;

    // Adjacent threads read adjacent spatial positions.
    // Keep all channel minima in registers.
    #pragma unroll
    for (int c = 0; c < CHANNELS; ++c) {
        const float* channel_input = batch_input + c * channel_stride;
        float minimum = CUDART_INF_F;

        #pragma unroll 1
        for (int64_t d = 0; d < depth; ++d) {
            const float value = channel_input[d * spatial];
            minimum = (value < minimum || isnan(value)) ? value : minimum;
        }

        values[c] = minimum;
        maximum = fmaxf(maximum, minimum);
    }

    float denominator = 0.0f;

    #pragma unroll
    for (int c = 0; c < CHANNELS; ++c) {
        values[c] = __expf(values[c] - maximum);
        denominator += values[c];
    }

    const float inverse = 1.0f / denominator;
    float* batch_output = out + batch * CHANNELS * spatial + p;

    #pragma unroll
    for (int c = 0; c < CHANNELS; ++c) {
        batch_output[c * spatial] = values[c] * inverse;
    }
}

torch::Tensor min_softmax_cuda(torch::Tensor x)
{
    TORCH_CHECK(x.is_cuda(), "Expected a CUDA tensor");
    TORCH_CHECK(x.scalar_type() == at::kFloat, "Expected float32");
    TORCH_CHECK(x.dim() == 5, "Expected NCDHW input");
    TORCH_CHECK(x.size(1) == 24, "Expected 24 channels");
    TORCH_CHECK(x.size(2) > 0, "Cannot reduce an empty depth dimension");
    TORCH_CHECK(x.is_contiguous(), "Expected contiguous input");

    const c10::cuda::CUDAGuard device_guard(x.device());

    const int64_t batch = x.size(0);
    const int64_t depth = x.size(2);
    const int64_t height = x.size(3);
    const int64_t width = x.size(4);
    const int64_t spatial = height * width;

    auto output = torch::empty({batch, 24, height, width}, x.options());
    if (output.numel() == 0) {
        return output;
    }

    constexpr int threads = 128;
    const dim3 blocks(
        static_cast<unsigned int>((spatial + threads - 1) / threads),
        static_cast<unsigned int>(batch));

    min_softmax_kernel<24><<<
        blocks, threads, 0, at::cuda::getCurrentCUDAStream()
    >>>(
        x.data_ptr<float>(),
        output.data_ptr<float>(),
        spatial,
        depth);

    C10_CUDA_KERNEL_LAUNCH_CHECK();
    return output;
}
"""

_fused_ops = load_inline(
    name="conv3d_depth_min_channel_softmax_v1",
    cpp_sources=_cpp_source,
    cuda_sources=_cuda_source,
    functions=["min_softmax_cuda"],
    extra_cflags=["-O3"],
    extra_cuda_cflags=["-O3"],
    verbose=False,
)


class ModelNew(nn.Module):
    def __init__(self, in_channels, out_channels, kernel_size, dim):
        super().__init__()
        self.conv = nn.Conv3d(in_channels, out_channels, kernel_size)
        self.dim = dim

    def forward(self, x):
        x = self.conv(x)

        if (
            x.is_cuda
            and x.dtype == torch.float32
            and x.ndim == 5
            and self.dim in (2, -3)
            and x.shape[1] == 24
            and x.shape[0] <= 65535
        ):
            return _fused_ops.min_softmax_cuda(x.contiguous())

        return torch.softmax(torch.min(x, dim=self.dim)[0], dim=1)
```